Question: Ben is 20 years older than Luis. For the last 3 years, Ben and Luis have been going to the same school. Nineteen years ago, Ben was 3 times as old as Luis. How old is Ben now?
Explanation: We can use the given information to write down two equations that describe the ages of Ben and Luis. Let Ben's current age be $b$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $b = l + 20$ Nineteen years ago, Ben was $b - 19$ years old, and Luis was $l - 19$ years old. The information in the second sentence can be expressed in the following equation: $b - 19 = 3(l - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $l$ and substitute it into our second equation. Solving our first equation for $l$ , we get: $l = b - 20$ . Substituting this into our second equation, we get the equation: $b - 19 = 3($ $(b - 20)$ $ -$ $ 19)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 19 = 3b - 117$ Solving for $b$ , we get: $2 b = 98$ $b = 49$.